A stone falls from the top of a building and hits the ground at the speed of 32m/s.
The air resistance-force on the stone is very small and may be negalected.
calculate the time of fall.
on fig 1.1 draw the speed-time graph for falling stone
the weight of the stone is 24N
Calculate the mass of the stone
To calculate the time of fall, we can use the formula for the time it takes for an object to fall from a height h:
t = √(2h/g)
where g is the acceleration due to gravity (9.8 m/s^2).
In this case, we know that the speed of the stone when it hits the ground is 32 m/s. Since the stone is falling, the final velocity (v) is equal to the initial velocity (u) plus the acceleration (g) times the time (t):
v = u + g*t
Using the equation for the time of fall, we can rewrite the above equation as:
32 m/s = 0 m/s + (9.8 m/s^2) * t
Simplifying the equation, we have:
32 m/s = 9.8 m/s^2 * t
Dividing both sides by 9.8 m/s^2:
t = 32 m/s / 9.8 m/s^2 ≈ 3.27 seconds
Therefore, the time of fall is approximately 3.27 seconds.
To draw the speed-time graph for the falling stone, we can create a graph with time (t) on the x-axis and speed (v) on the y-axis. The graph would be a straight line with a positive slope, indicating that the speed of the stone increases linearly with time.
Next, we can calculate the mass of the stone using the weight of the stone. The weight of an object can be calculated using the formula:
Weight = mass * gravity
In this case, we know that the weight of the stone is 24 N and the acceleration due to gravity is 9.8 m/s^2. Rearranging the equation, we have:
mass = weight / gravity
mass = 24 N / 9.8 m/s^2 ≈ 2.45 kg
Therefore, the mass of the stone is approximately 2.45 kg.